Adaptive polarization tracking and equalization in coherent optical receivers

ABSTRACT

A method for operating an optical receiver includes at each of a sequence of sampling times, producing a first 2D complex digital signal vector whose first component is indicative of a phase and amplitude of one polarization component of a modulated optical carrier and whose second component is indicative of a phase and amplitude of another polarization component of the carrier. For each one of the sampling times, the method includes constructing a second 2D complex digital signal vector that is a rotation of the first 2D complex digital vector for the one of sampling times. The rotation compensates a polarization rotation produced by transmission of the modulated optical carrier between an optical transmitter and the optical receiver.

BACKGROUND

1. Field of the Invention

The invention relates to coherent optical receivers and methods ofoperating coherent optical receivers.

2. Discussion of the Related Art

This section introduces aspects that may be helpful to facilitating abetter understanding of the inventions. Accordingly, the statements ofthis section are to be read in this light and are not to be understoodas admissions about what is in the prior art or what is not in the priorart.

In optical communication systems, a variety of schemes have beenconsidered for implementing coherent detection. While homodyne detectionis often desirable, there is a significant difficulty with implementinghomodyne detection in optical communications systems at high data rates.Homodyne detection involves phase locking to the received carrier, andphase locking is often complex to achieve for an optical carrier.Partially due to this deficiency of optical homodyne detection,heterodyne and intradyne detection have also been considered forcoherent optical receivers.

In intradyne detection, the receiver uses a local oscillator to down mixthe data-carrying carrier. Nevertheless, the local oscillator of thereceiver is not tightly phase or frequency locked to the data-carryingoptical carrier. Instead, the local oscillator of the receiver has afrequency that loosely configured to be closer to the frequency of thedata-carrying carrier than the bandwidth of the data-carrying carrier.Thus, an intradyne optical receiver would not typically have an opticalphase locked loop. Due to the absence of optical phase locked loops,intradyne optical receivers may offer advantages in coherent opticaldetection.

Coherent detection may be used to recover data transmitted via aphase-shift-keying (PSK) modulation scheme. Nevertheless, theperformance of a receiver of PSK modulated data is typically sensitiveto frequency offsets and carrier linewidths. For that reason,efficiently implementing an intradyne optical receiver for PSK modulatedoptical carriers has posed some challenges.

BRIEF SUMMARY

Various embodiments use digital signal processing to handle issuesassociated with recovering data from optical carriers that are modulatedvia phase-shift-keying (PSK). Through digital signal processing, someembodiments provide for adaptive polarization tracking, and someembodiments provide for adaptive equalization. Such digital signalprocessing may compensate for optical inter-symbol interference (OISI)even when the optical communications channel causes the carrier'spolarization to vary in time and/or introduces a polarization-dependentphase shift.

Herein, a hybrid optical detector has one or more optical ports forinputting light with one or more properties to be measured and includesone or more electrical output ports for outputting one or moreelectrical signals indicative of the value(s) of the one or moreproperties for the light input to the one or more optical ports.

One embodiment features an apparatus that includes an optical receiverconfigured to recover data from a PSK modulated optical carrier. Theoptical receiver includes an optical detector and a digital processor.The optical detector is configured to produce a sequence of vectorshaving first and second digital components. Each first component isindicative of a complex value of a first polarization component of themodulated optical carrier at a corresponding sampling time. Each secondcomponent is indicative of a complex value of a different secondpolarization component of the modulated optical carrier at the samplingtime. The digital processor is connected to receive the vectors and isconfigured to perform a rotation on each received vector individually ina manner that compensates for polarization rotations produced bytransmitting the modulated optical carrier from an optical transmitterthereof to the optical receiver.

In some embodiments of the apparatus, the digital processor isconfigured to iteratively update each angle of the rotation by an amountproportional to a difference between magnitudes of the components of avector produced by an earlier one of the rotations. The digitalprocessor may be configured to evaluate an error in the amplitude of oneof the components of the rotated vectors. The digital processor may beconfigured to equalize the first components of the rotated vectors basedon differential phase errors between successive ones of the firstcomponents of the rotated vectors. The digital processor may also beconfigured to equalize the second components of the rotated vectorsbased on differential phase errors between successive ones of the secondcomponents of the rotated vectors.

In some embodiments of the apparatus, the digital processor isconfigured to rotate the received vectors without performing crossequalization between the first and second components of the vectors.

In some embodiments of the apparatus, the processor is configured toperform the rotations in a manner that tends to equalize amplitudes ofthe first second components.

In some embodiments of the apparatus, the hybrid optical detectorincludes an optical hybrid configured to output first mixtures of themodulated optical carrier and a reference optical carrier at firstoutputs and to output second mixtures of the carriers having differentrelative phases at second outputs. In such embodiments, the digitalprocessor may be configured to equalize the first components of therotated vectors based on evaluated differential phase errors betweensuccessive ones of the first components of the rotated vectors.

Another embodiment features an apparatus including an optical receiverconfigured to recover data PSK modulated onto a received opticalcarrier. The optical receiver includes an optical detector and a digitalprocessor. The optical detector is configured to produce a sequence ofvectors having first digital electrical signal components. Each firstelectrical digital signal component is indicative of a value of onepolarization component of the received optical carrier at acorresponding sampling time. The digital signal processor is connectedto receive the first digital electrical signal components and toequalize the first digital electrical signal components in a mannerresponsive to differential phase errors between successive ones of thefirst digital electrical signal components.

In some embodiments of the apparatus, the optical detector is configuredto produce second digital electrical signal components of the vectors.Each second digital electrical signal component is indicative of a valueof another polarization component of the received optical carrier at thecorresponding sampling time. The digital processor may be configured toequalize the second digital electrical signal components in a mannerresponsive to differential phase errors between successive ones of thesecond digital electrical signal components.

In some embodiments of the apparatus, the digital processor may includea device configured to function as a FIR filter that equalizes the firstdigital electrical signal components by producing a weighted sum of(2L+1) successive ones of the first digital electrical signalcomponents, wherein L is greater than or equal to one. The digitalprocessor may also include a weight updating device that is configuredto update weights defining the sum based on the differential phaseerror.

Another embodiment features a method for operating an optical receiver.The method includes at each of a sequence of sampling times, producing afirst 2D complex digital signal vector whose first component isindicative of a phase and amplitude of one polarization component of amodulated optical carrier and whose second component is indicative of aphase and amplitude of another polarization component of the carrier.For each one of the sampling times, the method includes constructing asecond 2D complex digital signal vector that is a rotation of the first2D complex digital vector for the one of sampling times. The rotationcompensates a polarization rotation produced by transmission of themodulated optical carrier between an optical transmitter and the opticalreceiver.

In some embodiments, the method further includes iteratively updatingeach angle of the rotation by an amount proportional to a differencebetween magnitudes of the components of a vector produced by an earlierone of the rotations.

In some embodiments, the method further includes prior to one of theacts of constructing, updating a form of the rotation for the one of theacts of constructing such that said one of the acts of constructingproduces a second 2D complex digital signal vector whose first andsecond components have better equalized amplitudes.

In some embodiments, the method further includes equalizing firstcomponents of the second 2D digital signal complex vectors based ondifferential phase errors between successive ones of the firstcomponents of the second 2D complex digital signal vectors. The methodmay be such that the equalizing of each first component includesproducing a weighted sum of (2L+1) successive ones of the firstcomponents of the second 2D complex digital signal vectors, wherein L isgreater than or equal to one.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A, 1B, and 1C illustrate quadrature PSK (QPSK), eight PSK (8PSK),and sixteen PSK (16PSK) symbol constellations that may be implemented inthe embodiments described herein;

FIG. 2 is a block diagram illustrating an optical communication system;

FIG. 3A is a block diagram illustrating one embodiment of the coherentoptical receiver shown in FIG. 2;

FIG. 3B is a block diagram illustrating an alternate embodiment of thecoherent optical receiver of FIG. 2 that includes a single opticalhybrid;

FIG. 4 is a block diagram illustrating one embodiment of the hybridoptical detector of FIG. 3A;

FIG. 5A is a block diagram illustrating an embodiment of the digitalsignal processors (DSPs) of FIGS. 3A and 3B that compensates forpropagation-induced polarization rotations;

FIG. 5B is a block diagram illustrating an embodiment of the DSPs ofFIGS. 3A-3B that provides equalization;

FIG. 5C is a block diagram illustrating an embodiment of the DSP ofFIGS. 3A and 3B that both compensates for propagation-inducedpolarization rotations and provides equalization;

FIG. 5D is a block diagram illustrating an embodiment of the DSP ofFIGS. 3A and 3B that provides equalization in a optical communicationssystem without polarization multiplexing;

FIG. 5E is a block diagram illustrating an embodiment of the DSP ofFIGS. 3A and 3B that corrects propagation-induced polarization rotationsand provides equalization in a optical communications system withoutpolarization multiplexing;

FIG. 6 is a flow chart illustrating a process for updating the rotationangle that defines the polarization rotation done by the DSP of FIG. 5A;

FIG. 7 is a block diagram illustrating one structure for the ODLFequalizers in the DSP of FIG. 5B;

FIG. 8 is a block diagram illustrating one method of operating the ODLFequalizer illustrated by FIG. 7; and

FIG. 9 is a block diagram illustrating one method of updating the weightcoefficients of the FIR filter in the ODLF equalizer of FIG. 7.

In the Figures and text, like reference numerals indicate elements withsimilar functions.

In the Figures, the relative dimensions of some features may beexaggerated to more clearly illustrate one or more of the structurestherein.

Herein, various embodiments are described more fully by the Figures andthe Detailed Description of Illustrative Embodiments. Nevertheless, theinventions may be embodied in various forms and are not limited to theembodiments described in the Figures and Detailed Description ofIllustrative Embodiments.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

Methods and apparatus for optical data transmission and coherent opticalreception, which may be useful in embodiments herein, are described inU.S. patent application Ser. No. 11/204,607, which was filed on Aug. 15,2005, by Young-Kai Chen et al and is incorporated herein by reference inits entirety. Herein, this U.S. patent application of Y. K. Chen et alwill be referred to at the '607 application.

An optical receiver converts a received PSK modulated optical carrierinto a stream of digital data symbols. To efficiently do suchconversion, some embodiments of the intradyne optical receiversdescribed herein may include one or more specific adaptations. Onespecific adaptation is directed towards compensating for the lack offrequency and phase synchronization between the local optical oscillatorof the intradyne optical receiver and the modulated optical carrier.Another specific adaptation is directed towards compensating orcorrecting a lack of polarization lock between the optical receiver'slocal optical oscillator and the modulated optical carrier. One or morespecific adaptations are also directed towards compensating for orcorrecting one or more of the degradations to the modulated opticalcarrier, which are produced by the optical communications channel. Thesedegradations may include amplified spontaneous emission (ASE) noise,which is produced by in-line optical amplifiers and/or opticalinter-symbol interference, which may be caused by chromatic dispersionor polarization mode dispersion (PMD), and polarization rotations, whichwere caused by PMD.

FIGS. 1A-1C illustrate a few symbol constellations that may be used tomodulate data onto the optical carrier in optical communications systemsdescribed herein. The constellations include a quadrature PSK (QPSK)constellation of FIG. 1A, an eight PSK (8PSK) constellation of FIG. 1B,and a sixteen PSK (16PSK) constellation of FIG. 1C. The QPSK, 8PSK, and15 PSK constellations have 4, 8, and 16 symbols, respectively, which areshown as points (1), (2), . . . , (16) in the complex plane. In thevarious embodiments, the symbols of the selected PSK constellation aremodulated onto the phase of the optical carrier, i.e., as a factor ofthe form exp(iθ_(S)). For the QPSK, 8PSK, and 16PSK constellations, thevariable θ_(S) may belong to {0, π/2, π, 3π/2}, {0, π/4, π/2, 3π/4, π,5π/4, 3π/2, 7π/4}, and {0, π/8, π/4, 3π/8, . . . , 15π/8}, respectively.In various embodiments, the symbols of these PSK constellations may alsobe used to differentially encode data words with 2, 3, and 4 bits,respectively, e.g., as by the mappings of 2, 3, and 4 bit words in FIGS.1A-1C.

FIG. 2 illustrates generally an optical communications system 10 inwhich a PSK modulated optical carrier communicates the data. The opticalcommunications system 10 includes an optical transmitter 12, an opticalcommunications channel 14, and an optical receiver 16. The opticaltransmitter 12 modulates a continuous light wave to have a sequence ofsymbols in a selected PSK format, e.g., QPSK, 8PSK, or 16 PSK. Theoptical transmitter 12 may PSK modulate optical pulses having anon-return-to-zero (NRZ) or a return-to-zero (RZ) format. The opticaltransmitter 12 either modulates one PSK symbol stream onto the linearpolarization component(s) of the optical carrier or modulates anindependent PSK symbol stream onto each of the linear polarizationcomponents of the optical carrier. The later technique is known aspolarization multiplexing. The optical communications channel 14transports the PSK modulated optical carrier from the opticaltransmitter 12 to the optical receiver 16. The optical communicationschannel 14 may include a free-space optical link and/or a single ormulti-span optical or all-optical fiber transmission line. The opticalreceiver 16 recovers one or two estimated symbol streams from themodulated optical carrier that is received from the opticalcommunications channel 14, i.e., depending on whether the opticalcarrier has been polarization multiplexed.

FIG. 3A illustrates one embodiment of the optical receiver 16 of FIG. 2.The optical receiver 16 includes a local optical oscillator 18, twooptical polarization splitters 20, two 2×2 hybrid optical detectors 22_(V), 22 _(H), a digital signal processor (DSP) 24, and a plurality ofoptical waveguides (OWs) and electrical lines (ELs) that connectelements 18, 20, 22 _(V), 22 _(H), 24 therein. Herein, the letters “V”and “H” will be used to designate tow different linear polarizationcomponents, e.g., the mutually orthogonal “vertical” and “horizontal”components of a lab frame.

The local optical oscillator 18 produces a continuous-wave (CW)reference optical carrier at about the wavelength of the optical carrierthat is received from the optical communications channel 14. The localoptical oscillator 18 is a coherent light source, e.g., anenvironmentally stabilized diode laser. The local optical oscillator 18will frequency down-mix the received optical carrier in the hybridoptical detectors 22 _(V), 22 _(H). For that reason, the local opticaloscillator 18 is setup to output the reference optical carrier with afrequency, ω_(RC), that is approximately equal to the frequency, ω_(MC),of the modulated optical carrier received from the opticalcommunications channel 14. Nevertheless, the optical receiver 16 doesnot have an optical phase lock loop (PLL) that tightly locks the phaseof CW reference optical carrier to the phase of the modulated opticalcarrier that is received from the optical communications channel 14.Indeed, line widths of the light from the local optical oscillator 18and/or the optical transmitter 12 may produce frequency variationssufficient to destroy any such tight phase synchronization between themodulated and reference optical carriers. Thus, the reference opticalcarrier and modulated optical carrier may have a phase offset thatdrifts substantially in time.

Even in the absence of frequency locking, some embodiments of theoptical receiver 16 may be able to function as intradyne detectors. Inthese embodiments, the optical transmitter 12 may use, e.g., afrequency-stabilized light source to produce the optical carrier, andthe local optical oscillator 18 may use, e.g., a frequency-stabilizedlight source to produce the reference optical carrier.

The two optical polarization splitters 20 separate the reference opticalcarrier from the local optical oscillator 18 and the modulated opticalcarrier from the optical communications channel 14 into linearpolarization components “H” and “V”, which are substantially orthogonal,e.g., the “vertical” and “horizontal” components in a lab frame. Eachoptical polarization splitter 20 transmits light of the V linearpolarization component to one optical input of the 2×2 hybrid opticaldetector 22 _(V) and transmits light of the substantially orthogonal Hlinear polarization to one optical input of the other 2×2 hybrid opticaldetector 22 _(H). Thus, each 2×2 hybrid optical detector 22 _(V), 22_(H) receives light from the local optical oscillator 18 on one of itsoptical inputs and receives light from the optical communicationschannel 14 on the other of its optical inputs.

The hybrid optical detectors 22 _(V), 22 _(H) coherently mix lightreceived at their optical inputs and output digital measures of theresulting mixtures at their electrical outputs. In particular, eachhybrid optical detector 22 _(V), 22 _(H) outputs a complex digitalsignal value at its electrical outputs. The complex digital signal valueis indicative of the complex amplitude of the corresponding polarizationcomponent of the modulated optical carrier as frequency down-mixed bythe reference optical carrier, i.e., the complex digital signal includesamplitude and phase information. The hybrid optical detectors 22 _(V),22 _(H) produce the complex digital signal values by sampling electricalsignal levels of optical detectors therein, i.e., at a samplingfrequency that is the modulated frequency of the optical carriergenerated by the optical transmitter 12 or an integer multiple thereof.In the k-th sampling period, the hybrid optical detectors 22 _(V) and 22_(H) output respective complex digital signal values that will bereferred to as Y_(V)(k) and Y_(H)(k) whereY_(V)(k)=Re[Y_(V)(k)]+i·Im[Y_(V)(k)] andY_(H)(k)=Re[Y_(H)(k)]+i·Im[Y_(H)(k)].

The DSP 24 constructs one or more output streams of estimated digitalsymbols, i.e., D(k)s, from the one or two streams of complex digitaldata values output by the hybrid optical detectors 22 _(V), 22 _(H),i.e., the streams of Y_(V)(k)s and Y_(H)(k)s. In the output stream, eachD(k) is an estimate of a symbol of a PSK constellation that is carriedby the modulated optical carrier at a modulation period “k”. The DSP 24may perform various types of digital processing on the streams ofcomplex digital signal values, i.e., the streams Y_(H)(k), Y_(H)(k+1), .. . and Y_(V)(k), Y_(V)(k+1), . . . , to produce the one or more outputstream of estimated symbols. The digital processing may compensate foror correct signal degradations that are due to, e.g., PMD, chromaticdispersion, noise, and/or linewidths of the optical transmitter 12 andlocal optical oscillator 18.

FIG. 4 illustrates a hybrid optical detector 22 _(X) that is configuredto detect a QPSK modulated optical carrier, e.g., an exemplaryembodiment of the hybrid optical detectors 22 _(V), 22 _(H) of FIG. 3.Here and below, the subscript “X” may refer to either the “H” linearpolarization component or the “V” linear polarization component asappropriate. The hybrid optical detector 22 _(X) includes an opticalhybrid (OH) and first and second optical detectors that measure lightintensities output by the optical hybrid OH via digital sampling.

The optical hybrid includes two 1×2 optical intensity splitters 28A,28B; an optical phase delay 30; and two 2×2 optical mixers 32A, 32B aswell as optical waveguides OW connected to various ones of theseelements. The optical hybrid produces at two pairs of optical outputs,e.g., the pair (1, 2) and the pair (3,4), interfered mixtures of themodulated and reference optical carriers. The relative intensities ofthe mixtures at the two outputs of each pair are sensitive to relativephases of the light interfered. The relative phases of the interferedmixtures are different at the first pair (1, 2) of optical outputs thanat the second pair (3, 4) of optical outputs. Exemplary optical hybridsthat may be suitable for the optical receivers 16, 16′ of FIGS. 1A, 1B,and 2 are described, e.g., in U.S. patent application Ser. No.11/426,191, entitled “System And Method For Receiving Coherent,Polarization-Multiplexed Optical Signals”, which was filed by NoriakiKaneda and Andreas Leven on Jun. 23, 2006 and is incorporated herein byreference in its entirety.

Each optical detector includes one pair 34A, 34B of matched photodiodes36A, 36B; a differential amplifier 38A, 38B; and analog-to-digitalconverters 40A, 40B as well as electrical lines EL interconnectingvarious ones of these elements. Each optical detector measures theoptical signals at one pair of the optical outputs of the optical hybridOH, i.e., the pair (1,2) or the pair (3, 4). Indeed, each opticaldetector produces a sequence of digital electrical values by samplingthe intensities of the interfered carriers at one pair of the opticaloutputs of the optical hybrid.

Each of the 1×2 optical intensity splitters 28A, 28B power splitsreceived light so that about 50 percent of said light is directed toeach of its optical outputs. One of the 1×2 optical intensity splitters28A is connected to receive and power split light from the local opticaloscillator 18. The other of the 1×2 optical intensity splitters 28B isconnected to receive and power split light of the modulated opticalcarrier that is received from the optical communications line 14. Each1×2 optical intensity splitter 28A, 28B connects by an optical waveguideOW to deliver light to an optical input of the 2×2 optical mixer 32A andconnects by another optical waveguide OW to deliver light to an opticalinput of the other 2×2 optical mixer 32B.

Then, the optical phase delay 30 and waveguides OW introduce a relativephase delay, Δ, between the light transmitted from the 1×2 opticalsplitter 28B to the 2×2 optical mixer 32A and the light transmitted fromthe 1×2 optical splitter 28B to the 2×2 optical mixer 32B. Typically,the relative phase delay, Δ, is between π/3 and 2π/3 modulo Nπ. Therelative phase delay, Δ, is preferably between 3π/8 and 5π/8 modulo Nπand is more preferably about π/2 modulo Nπ. Here, N is an integer. Incontrast, the other optical waveguides OW do not introduce a substantialrelative phase delay, i.e., modulo Nπ, between the light transmittedfrom the other optical intensity splitter 28A to the optical mixer 32Aand the light transmitted from the other optical intensity splitter 28Ato the optical mixer 32B.

Alternately, the optical phase delay 30 may be connected to one of theoptical outputs of the 1×2 optical splitter 28A rather than to one ofthe optical outputs of the 1×2 optical splitter 28B (not shown). Then,the optical phase delay 30 would introduce a relative phase delay, A,between light transmitted from the 1×2 optical splitter 28A to the 2×2optical mixer 32A and the light transmitted from the 1×2 opticalsplitter 28A to the 2×2 optical mixer 32B. Such a relative phase delay,Δ, is between π/3 and 2π/3 modulo Nπ. The relative phase delay, Δ, ispreferably between 3π/8 and 5π/8 modulo Nπ and is more preferably aboutπ/2 modulo Nπ. Here, N is an integer. In such embodiments, the opticalwaveguides OW between the other optical intensity splitter 28B and theoptical mixers 32A, 32B introduce substantially no relative phase delay,i.e., modulo Nit, between the light delivered to the two optical mixers32A, 32B.

In the hybrid optical detector 22 _(X), each of the 2×2 optical mixers32A, 32B is connected to receive the same linear polarization componentof the modulated optical carrier and the reference optical carrier. Theoptical mixers 32A, 32B mix, i.e., interfere, the light received attheir optical inputs to produce preselected combinations of said lightat their optical outputs. The optical mixers 32A, 32B may be, e.g.,conventional or multi-mode interference (MMI) devices.

The 2×2 optical mixers 32A, 32B produce frequency down-mixed versions ofthe modulated optical carrier. The first optical mixer 32A mixes thelight received its optical inputs so that the difference between thelight intensities at its optical outputs is indicative of the phasedifference, i.e., (φ+t·[ω_(MC)−ω_(RC)]), between the light received fromthe optical communications channel 14 and the light received from thelocal optical oscillator 18. Here, ω_(MC) and ω_(LC) are the frequenciesof the modulated optical carrier and the reference optical carrier,respectively, “t” is time, and φ is a phase offset. In particular, thelight intensity at the first optical output 1 of the first optical mixer32A minus the light intensity at the second optical output 2 of thefirst optical mixer 32A is proportional to the amplitudes of the lightat the two optical inputs of the first optical mixer 32A times arelative phase dependent factor, e.g., sin(φ+t·[ω_(MC)−ω_(RC)]).Similarly, the second optical mixer 32B also mixes the light received atits optical inputs so that the difference between the light intensitiesat its optical outputs 3, 4 is indicative of the phase difference, i.e.,(φ+t·[ω_(MC)−ω_(RC)]), between the light received from the opticalcommunications channel 14 and the light received from the local opticaloscillator 18. In particular, if the above-discussed relative phasedelay Δ is π/2 mode 2Nπ where N is an integer, then, the light intensityat the first optical output 3 of the second optical mixer 32B minus thelight intensity at the second optical output 4 of the second opticalmixer 32B is proportional to the amplitudes of the light at the twooptical inputs of the second optical mixer 32B times a differentrelative phase dependent factor, e.g., cos(φ+t·[ω_(MC)−ω_(RC)]).

At each optical output 1-4 of the 2×2 optical mixers 32A, 32B, acorresponding photo-diode 36A, 36B is positioned to detect the intensityof the output light. The photo-diodes form two pairs 34A, 34B ofbalanced or matched light-sensitivity. In the pairs 34A, 34B, eachphoto-diode 36A, 36B generates at one input of a differential amplifier38A, 38B a voltage or a current indicative of the detected lightintensity.

Each differential amplifier 38A, 38B outputs an analog voltage, i.e.,V_(X,1) or V_(X,2), proportional to a voltage difference applied to itstwo inputs.

From the analog voltages V_(X,1) and V_(X,2), the first and second A/Dconverters 40A, 40B produce respective first and second temporalsequences of digital signal values, i.e., Y_(X,1)(k), Y_(X,1)(k+1), . .. and Y_(X,2)(k), Y_(X,2)(k+1), . . . . To produce these sequences, theA/D converters 40A, 40B sample the analog voltages V_(X,1) and V_(X,2)at sampling rate that may be equal to the symbol/modulation rate or maybe an integer multiple of the modulation/symbol rate. The A/D converters40A, 40B transmit the digital signal values Y_(X,1)(k) and Y_(X,2)(k) tothe DSP 24 at the k-th sampling period.

Each complex digital signal value Y_(X)(k)=Y_(X,1)(k)+iY_(X,2)(k) can bemodeled as having the form:

Y _(X)(k)=B _(X)(k)·exp[i·φ _(X)(k)]+N _(X)(k).  (1)

In the above equation, B_(X)(k) and φ_(X)(k) are the amplitude andphase, and N_(X)(k) is a noise at sampling period “k”. The phaseφ_(X)(k) may be represented as Φ_(B)(k)+Φ_(S)(k)+k·T·(ω_(MC)−ω_(RC))where T is the sampling period, Φ_(B)(k) is the phase for a PSK symbol,and Φ_(S)(k) is an aggregate phase noise. The aggregate phase noiseΦ_(S)(k) may obtain substantial contributions due to the line width ofthe optical transmitter 12 and/or of the local optical oscillator 18 ofFIGS. 2-3.

Referring again to FIG. 3, the DSP 24 processes a 2D complex digitalvector Y(k), i.e., Y(k)=[Y_(V)(k), Y_(H)(k)]^(T) at each sampling period“k”. (Herein, superscripts “^(†)” and “^(T)” mean Hermetian conjugationand matrix transposition, respectively.) The vector Y(k) corresponds toa 2D vector P(k) whose components are the actual modulation phases thatthe optical receiver 16 is attempting to recover from the receivedmodulated optical carrier. That is, P(k)=[P_(V)(k), P_(H)(k)]^(T) wherethe phases P_(V)(k) and P_(H)(k) were modulated by the opticaltransmitter 12 onto the respective “V” and “H” polarization componentsof the optical carrier at a corresponding modulation time. Due totransmission and reception signal degradation, the vector Y(k) oftendiffers from the original vector P(k). The DSP 24 may perform varioustypes of digital processing of the Y(k)s to recover better estimates ofthe original P(k)s.

FIG. 3B illustrates an alternate embodiment for an optical receiver 16′.The optical receiver 16′ is an optical detector that includes a localoptical oscillator 18; a single optical hybrid OH; four opticalpolarization splitters 20, four pairs 34A, 34B of matched or balancedphoto-diodes 36A, 36B; four differential amplifiers 38A, 38B; DSP 24;and optical waveguides OW and electrical lines EL connecting saidelements. In the optical receiver 16′, each element has a similarconstruction and/or function as the similarly referenced elements of theoptical receiver 16 of FIGS. 3A and 4, e.g., elements referenced as 18,20, 34A, 34B, 36A, 36B, 38A, 38B, OW, EL. Also, the optical receiver 16′receives and outputs similar optical and electronic signals. Inaddition, the digital sampled values Y_(V, 1)(k), Y_(V, 2)(k),Y_(H, 1)(k), Y_(H, 2)(k) that are transmitted to the DSP 24 are similarin the optical receiver 16 and the optical receiver 16′. For thatreason, both optical receivers 16, 16′ can have substantially identicalDSPs 24.

The optical receiver 16′ performs polarization splitting at opticaloutputs 1, 2, 3, 4 of the optical hybrid OH rather than prior totransmitting light thereto. Each optical polarization splitter 20transmits the two polarization components of the light from one opticaloutput 1, 2, 3, 4 of the optical hybrid OH to different photo-diodes36A, 36B. For that reason, the optical receiver 16′ has a single opticalhybrid OH rather than two optical hybrids OH as in the optical receiver16 of FIGS. 1A and 2.

In the optical receiver 16′, the optical hybrid OH may be a bulk opticalhybrid rather than a planar optical hybrid OH as illustrated in FIG. 4.Suitable bulk optical hybrids are commercially sold by OptoplexCorporation of 3374-3390 Gateway Boulevard, Fremont, Calif. 94538,United States (online at www.optiplex.com).

With respect to the optical receivers 16, 16′ of FIGS. 3A and 3Bexemplary types of digital processing therein are illustrated byspecific embodiments of DSPs 24A, 24B, 24C, 24D, 24E shown in FIGS.5A-5E.

Referring to FIGS. 5A and 5C, the DSPs 24A, 24C include a polarizationtracking unit (PolTrack) 44. The PolTrack unit 44 performs a lineartransformation on each received 2D complex vector Y(k) individually toproduce a 2D complex vector Z(k), i.e., Z(k)=[Z_(V)(k),Z_(H)(k)]^(T).The linear transformation is given by:

Z(k)=J(k)·Y(k).  (2)

Here, the 2×2 matrix J(k) performs a rotation. Thus, the components ofJ(k) are:

J ₁₁ =J ₂₂=cos[θ(k)] and J ₂₁ =−J ₁₂=sin[θ(k)].  (3)

The single rotation angle θ(k) defines the matrix. J(k). The rotationangle θ(k) is regularly updated to track changes that are caused by atemporal evolution of the optical communications channel 14. Theupdating of the rotation angle θ(k) is configured so that the “V” and“H” components of the rotated vector Z(k) and the original phasemodulation vector P(k) remain substantially aligned. In particular, thePolTrack unit 44 transforms the Y(k)s to track polarization rotationsproduced by propagation from the optical transmitter 12 through theoptical communications channel 14.

FIG. 6 illustrates a method 50 for dynamically updating the rotationangle θ(k). For example, the PolTrack unit 44 may be configured toperform the updating method 50. The PolTrack unit 44 may perform themethod 50 during each sampling period during ordinary operation or mayperform the method 50 to update θ(k) less frequently.

For each update of the rotation angle θ(k), the method 50 includesevaluating a gradient with respect to the rotation angle θ(k) of a sumof the squared power errors in the components of the 2D complex digitalsignal vector Z(k) last produced by the PolTrack unit 44 (step 52). The“V” and “H” components of Z(k) have respective power errors e_(V)(k) ande_(H)(k), which are given by:

e _(V)(k)=|P _(V)(k)|² −|Z _(V)(k)|²=1−|Z _(V)(k)|² and

e _(H)(k)=|P _(H)(k)|² −|Z _(H)(k)|²=1−|Z _(H)(k)|².  (4)

Above, the second forms for the power errors follow, because P_(V)(k)and P_(H)(k) are phases up to a constant amplitude, which has been takenas one. From the above definition of Z(k), the θ(k)-gradients ofe_(V)(k) and e_(V)(k) can be shown to satisfy:

$\begin{matrix}\begin{matrix}{{\partial_{\theta {(k)}}\left\lbrack {e_{H}(k)} \right\rbrack} = {- {\partial_{\theta {(k)}}\left\lbrack {e_{V}(k)} \right\rbrack}}} \\{{\left. {{{= {\left\lbrack  \right.{Y_{H}(k)}}}}^{2} - {{Y_{V}(k)}}^{2}} \right\rbrack \cdot {\sin \left\lbrack {2{\theta (k)}} \right\rbrack}} - {2 \cdot}} \\{{{{Re}\left\lbrack {{{Y_{V}(k)} \cdot Y_{H}}*(k)} \right\rbrack} \cdot {{\cos \left\lbrack {2{\theta (k)}} \right\rbrack}.}}}\end{matrix} & (5)\end{matrix}$

The gradient with respect to the rotation angle θ(k) of the sum of thesquared power errors of the 2D complex vector Z(k) is∂_(θ)[(e_(H)(k))²+(e_(V)(k))²]. From eqs. (4)-(5), this expression maybe seen to satisfy:

∂_(θ)[(e _(H)(k))²+(e _(V)(k))² ]=γ[|Z _(V)(k)|² −|Z _(H)(k)|²]∂_(θ) [e_(H)(k)].  (6)

The performance of step 52 may include evaluating ∂_(θ)[e_(H)(k)] witheq. (5) and the, using the value of ∂_(θ)[e_(H)(k)] to evaluate theright hand side of eq. (6).

For each update of the rotation angle θ(k), the method 50 includesupdating the last rotation angle θ(k) by an amount that is proportionalto the evaluated gradient of the squared power errors for the twocomponents of the last evaluated vector Z(k) (step 54). From above eq.(6), the step 54 includes performing on the rotation angle the iterativeupdate:

θ(k+1)=θ(k)+γ[|Z _(V)(k)|² −|Z _(H)(k)|²]∂_(θ) [e _(H)(k)].  (7)

Here, γ is a preselected positive number that fixes the size of anupdate step. From eq. (7), the update step 54 involves adding acorrection to θ(k), wherein the correction is proportional to adifference between |Z_(V)(k)| and |Z_(H)(k)|, i.e., the update isproportional to |Z_(V)(k)|−|Z_(H)(k)|. The updated rotation angle willbe used by the PolTrack unit 44 to rotate the next complex digitalsignal vector Y(k) that is received from the hybrid optical detectors 22_(V), 22 _(H).

The above method 50 updates the rotation angle θ(k) in a mannerconfigured to equalize energies of the polarization components of thevector Z(k) produced by the PolTrack unit 44.

In addition, neither the polarization tracking transformation of eq. (1)nor the update method 50 involve equalization. For example, eachiterative update of the rotation angle θ(k) is based on energy errors ofone earlier sampling period. Also, the rotation of eq. (1) does notinvolve the equalization of individual polarization components of thecomplex digital signal vector Y(k). In particular, the performance ofthe method 50 does not includes cross equalization of the twopolarization components Y_(V)(k) and Y_(H)(k) of the complex digitalsignal vector Y(k) together. During performance of the method 50,neither polarization component of the vector Y(k) gets replaced by aweight sum of the component of the digital signal vector Y(k) at earliersampling times wherein the sum includes the other polarizationcomponent. Due to the lack of a reliance on equalization, the PolTrackunit 44 can be a simpler and faster hardware device.

As illustrated by eqs. (5) and (7), the method 50 does not requireknowledge of the specific phase data being transmitted. For that reason,the method 50 may be implemented without transmission of a preselectedsequence of training symbols. Indeed, the PolTrack unit 44 mayeffectively implement the method 50 whether the symbol sequencesmodulated onto the “V” and “H” polarization components are the same orindependent sequences. With the method 50, the PolTrack unit 44 canoperate effectively when the optical transmitter 12 polarizationmultiplexes data onto the transmitted optical carrier and can otherwiseaid to implement a polarization-diverse embodiment of the opticalreceiver 16.

Referring to FIG. 5B, the DSP 24B includes two optical lineardifferential filter (OLDF) equalizers 46V, 46H. Optionally, the DSP 24Bincludes a symbol estimate combiner (SEC) 48, e.g., for embodiments ofoptical receivers 16, 16′ configured to receive modulated opticalcarriers on which data is not polarization multiplexed. The ODLFequalizer 46V processes the sequence of 2D complex digital Y_(V)(k)s toproduce a sequence of complex digital D_(V)(k)s in which the temporalbroadening effects of optical inter-symbol interference (OISI) arereduced. The ODLF equalizer 46H processes the sequence of complexdigital Y_(H)(k)s to produce a sequence of complex digital D_(H)(k)s inwhich the temporal broadening effects of OISI are reduced. The ODLFequalizers 46V, 46H are illustrated in FIG. 7 where “X” refers to the“V” or “H” linear polarization components as appropriate.

FIG. 7 illustrates an exemplary structure for the ODLF equalizer 46X.The ODLF equalizer 46X includes a finite impulse response (FIR) filter60, a weight updating device (WUD) 62, one sample period delays (D), anda serial-load parallel-output shift register (SR) 64. From theY_(X)(k)s, the FIR filter 60 produces equalized complex D_(X)(k)s viamethod 70 of FIG. 8. In addition, the WUD 62 performs updates of the(2L+1) complex coefficients of the FIR filter 60, i.e., the coefficientsC_(X,−L)(k), . . . , C_(X,0)(k), . . . , C_(X,+L)(k), via a method 82 ofFIG. 9. Such updates of the coefficients of the FIR filter 60 are doneregularly so that equalization performed by the ODLF equalizer 46Xtracks changes in the optical communications channel 14.

FIG. 8 describes the method 70 for performing equalization with the ODLF46X of FIG. 7. The method 70 includes serially receiving the sequence ofthe appropriate complex digital signal values, i.e., the Y_(X)(k)s, froman optical hybrid OH in the optical receiver 16, 16′ of FIG. 3A or 3B(step 72). The method 70 includes evaluating an equalized complexdigital signal value D_(X)(k) for each received complex digital signalvalue Y_(X)(k), e.g., one D_(X)(k) may be evaluated for each of theY_(X)(k)s (step 74). The evaluating step 74 involves forming a weightedaverage of (2L+1) of the consecutively received complex digital signalvalues. That, is the sum is a weighted average over the (2L+1)temporally neighboring values, e.g., the values Y_(X)(k−L), . . . ,Y_(X)(k+L). Here, L is a positive integer defining the width of theequalization region. In particular, the FIR filter 60 may evaluate eachequalized complex digital signal value D_(X)(k) as the weighted averagedefined by:

D _(X)(k)=C _(X)(k)^(†) ·Y _(X)(k)=Σ^(L) _(j)=_(−L) [C _(X,j)*(k)·Y_(X)(k−j)].  (8)

In above eq. (8), the (2L+1) dimension complex vectors C_(X)(k) andY_(X)(k) are given by:

C _(X)(k)=[C _(X,−L)(k), . . . , C _(X,+L)(k)]^(T) and  (9)

Y _(X)(k)=[Y _(X)(k+L), . . . , Y _(X)(k−L)]^(T).  (10)

In eqs. (9) and (10), the complex weight vector C_(X)(k) has components,i.e., C_(X,−L)(k), . . . , C_(X,+L)(k), which are the weightcoefficients of the FIR filter 60. In light of the above disclosure, oneof skill in the art would be able to make fabricate an exemplary FIRfilter 60 suitable to form the weighted average of eq. (8). The method70 also includes determining whether the equalized complex digitalsignal value(s) evaluated for each modulation period, i.e., one or moreD_(X)(k)s, correspond(s) to a modulation phase P_(X)(k) of a symbol in atraining sequence (step 76). If the evaluated complex digital signalvalue(s) correspond(s) to an estimate of a modulation phase P_(X)(k) ofa symbol in a training sequence, the method 70 includes transmitting theevaluated equalized complex digital signal value(s), i.e., the one ormore D_(X)s, to the WUD 62 for use in updating the weight coefficientsof the FIR filter 60 (step 78). Otherwise, the evaluated equalizedcomplex digital signal value(s) form(s) one or more estimates of amodulation phase factor P_(X)(k) for a data-carrying symbol. In thatcase, the method 100 then, includes outputting the evaluated equalizedcomplex digital signal value(s), i.e., the one or more D_(X)(k)s, foruse in estimating the data-carrying symbol corresponding to themodulation phase factor P_(X)(k) (step 80).

If the optical transmitter 12 does not modulate independent sequences ofPSK symbols onto the “V” and “H” polarization components of the opticalcarrier, the optional SEC 48, as shown in FIG. 5B, may combine orcompare the estimated modulation phases from the two ODLF equalizers46V, 46H, e.g., to provide polarization diversity. For example, theprocessing by the SEC 48 may obtain an improved estimate D(k) for theactual symbol that was modulated onto the optical carrier during thecorresponding modulation period. The optional SEC 48 may also combinesuch estimated phases for modulated symbols over more than one samplingperiod that corresponds to the same modulation period to produce theimproved estimate D(k) for the actual modulated symbol value.

FIG. 9 describes the method 82 for updating the coefficients of the FIRfilter 60 of FIG. 7.

The method 82 includes evaluating in the WUD 62 of FIG. 7 a differentialequalization error E_(X)(k) that measures the error between estimatedand actual values of training symbols (step 84). The WUD 62 obtains theestimated values output by the FIR filter 60, i.e., at above-describedstep 78 of the method 70. The WUD 62 may obtain the actual modulationphases P_(X)(k) and P_(X)(k−1), which have preselected values, from theDSP 24B. Both the D_(X)(k)s and P_(X)(k)s are, e.g., N-th roots ofunity, wherein N is the size of PSK constellation. One exemplarydefinition for such a differential equalization error E_(X)(k) is givenby:

$\begin{matrix}\begin{matrix}{{E_{X}(k)} = {{{P_{X}(k)} \cdot {P_{X}^{*}\left( {k - 1} \right)}} - {{D_{X}(k)} \cdot {D_{X}\left( {k - 1} \right)}}}} \\{= {{{P_{X}(k)} \cdot {P_{X}\left( {k - 1} \right)}^{*}} - {{C_{X}(k)}^{\dagger} \cdot {Y_{X}(k)} \cdot {Y_{X}\left( {k - 1} \right)}^{\dagger} \cdot}}} \\{{{C_{X}\left( {k - 1} \right)}.}}\end{matrix} & (11)\end{matrix}$

Since the error E_(X)(k) is a temporal differential function, a smallmismatch between the frequency, ω_(MC), of modulated optical carrier andthe frequency, ω_(RC), of the reference optical carrier typically willnot typically lead to a large magnitude for E_(X)(k). For that reason,such a differential error is believed to provide an adequate measure ofequalization-related mismatches even in the absence optical phase orfrequency locking between the modulated optical carrier and thereference optical carrier.

Next, the method 82 includes determining updated values for the(2L+1)-dimensional complex weight vector C_(X)(k). The updated valuesare based on the evaluated differential equalization error E_(X)(k) andalready estimated and/or received digital signal values (step 86). Forexample, the step 82 may update the complex weight vector C_(X)(k) ateach modulation period or at each sampling period as follows:

C _(X)(k+1)=C _(X)(k)−β·E _(X)(k)*·D _(x)*(k−1)·Y _(X)(k).  (12)

Here, β is a positive number defining the update step size.

The method 82 includes loading into the FIR filter 60 the updatedcomplex weight coefficient vector C_(X)(k+1) that was found at the step86 (step 88). The loaded weight coefficients will then, be used for thenext digital equalization performed by the FIR filter 60.

The method 82 includes determining whether the equalized complex digitalsignal value next to be outputted by the FIR filter 60, e.g.,D_(X)(k+1), corresponds to an estimated modulation phase of anothertraining symbol, i.e., a training symbol for a new modulation period(step 90). If the next outputted complex digital value does or willcorrespond to such a new training symbol, the method 82 includes loopingback 92 to again perform the step 84. Such loop backs 92 can improvevalues of the weight coefficients loaded onto the FIR filter 60, e.g.,by iteratively reducing the above-described differential equalizationerror. Otherwise, the method 82 includes outputting the equalizedcomplex digital signal value D_(X)(k+1) as an estimated modulation phasefor a data-carrying symbol carried by the modulated optical carrier,i.e., as at the step 80, and then, returning the ODLF equalizer 46X tothe mode of performing equalization according to the method 70 of FIG. 8(step 94).

In the method 80 for updating the complex weight coefficients of the FIRfilter 60, the differential error E_(X)(k) has several desirableproperties. First, the error E_(X)(k) is independent of any constantphase shift between the modulated optical carrier and the referenceoptical carrier. Second, the error E_(X)(k) is substantially independentof small line width-induced phase rotations provided that the samplingperiod is sufficiently short. For these reasons, the ODLF equalizer 46Xcan compensate OISI induced by the optical communications channel 14even in the absence of optical phase locking between the receivedmodulated optical carrier and the reference optical carrier. It is oftendesirable to avoid such an OPLL, because implementations of OPLLs can bedifficult to achieve at optical communications frequencies. The adaptiveequalizer 46X provides one way to provide for coherent optical detectionwithout such an undesirable OPLL.

FIG. 5C illustrates the DSP 24C, which combines the PolTrack unit 44 ofFIG. 5A and the DSP 24B of FIG. 5B thereby providing compensation forboth polarization rotation and OISI that occur in the opticalcommunications channel 14. In the DSP 24C, the PolTrack unit 44functions as described with respect to FIG. 5A. In the DSP 24C, eachODLF equalizer 46V, 46H functions like the ODLF equalizer 46X of FIGS.5B and 7-9, wherein digital signal values Z_(V)(k) and Z_(H)(k) from thePolTrack unit 44 replace the digital signal values Y_(V)(k) and Y_(H)(k)from the hybrid optical detectors 22 _(V), 22 _(H).

Combining the PolTrack unit 44 and the DSP 24B can also provide somelevel of compensation for PMD-induced phase shifts between the “V” and“H” polarization components of the modulated optical carrier. ThePolTrack unit 44 cannot of itself compensate for suchpolarization-dependent phase shifts. Such phase shifts between the “H”and “V” polarization components may be produced as the modulated opticalcarrier propagates through the optical communications channel 14. Theindependent equalization of the “H” and “V” polarization components inthe ODLF equalizer 46H and the ODLF equalizer 46V, respectively, mayprovide sufficient compensation for such polarization-dependent phaseshifts.

FIG. 5D illustrates the DSP 24D, which includes only one ODFL equalizer46V of FIG. 5B. In the DSP 24D, the ODLF equalizer 46V functions as inthe ODLF equalizer 46X of FIG. 5B. The DSP 24D can correct for OISI inthe optical communications channel 14 when the modulated optical carrieris not polarization multiplexed.

FIG. 5E illustrates the DSP 24E, which includes the PolTrack unit 44 andone ODFL equalizer 46V shown in FIG. 5C. In the DSP 24E, the PolTrackunit 44 and ODLF equalizer 46V functions as in the DSP 24C of FIG. 5C.The DSP 24E may correct polarization rotations and OISI in some opticalcommunications channels 14 when the modulated optical carrier is notpolarization multiplexed.

Referring again to FIG. 2, some optical communications channels 14 mayproduce high levels of optical noise, e.g., due to in-line opticalamplifiers. In these optical communications channels 14, equalizationbased on differential phase errors, i.e., based on the E_(X)(k)s, maynot adequate optimal equalization. For such optical communicationschannels 14, the ODLF equalizer 46X of FIG. 7 may be coupled serially tothe input of another equalizer. This other equalizer could be configuredto recursively estimate the phases modulated onto the received opticalcarrier based on the equalized complex signal values output by the ODLFequalizer 46X, i.e., the D_(X)(k)s. In such embodiments, the recursivelyestimated phases might also be feed back to the WUD 62 for use inupdating the weight coefficients of the FIR filter 60. Digitalprocessing methods and apparatus for such recursive estimates ofmodulation phases are described, e.g., in U.S. patent application Ser.No. 11/483,280, entitled “Recursive Phase Estimation for aPhase-Shift-Keying Receiver”, which was filed on Jul. 7, 2006 by Ut-VaKoc. This U.S. patent application is incorporated by reference herein inits entirety.

In light of the description and drawings herein, it may be evident toone of skill in the art that the DSP 24 of FIG. 3 could use a differentmethod to compensate polarization rotation and/or reduce the OISI thathas been produced by the optical communications channel 14. For example,such other methods could use different error measures than thosedescribed with respect to FIGS. 5A-5C and 6-9.

In some embodiments of the DSPs 24 of FIGS. 3A and 3B, a first or secondstage of signal processing may include a correction for phase errorscaused by the frequency offset between the modulated optical carrier andthe reference optical carrier. Devices for performing such correctionmay be useful in the optical receivers 16, 16′ and are described, e.g.,U.S. patent application Ser. No. 11/______, entitled “FrequencyEstimation In An Intradyne Optical Receiver”, which is being filed byAndreas Leven et al on the same date as this patent application and isincorporated herein by reference in its entirety.

From the above disclosure, the figures, and the claims, otherembodiments will be apparent to those of skill in the art.

1. An apparatus, comprising: an optical receiver configured to recoverdata from a PSK modulated optical carrier, the optical receivercomprising: an optical detector configured to produce a sequence ofvectors having first and second digital components, each first componentbeing indicative of a complex value of a first polarization component ofthe modulated optical carrier at a corresponding sampling time, and eachsecond component being indicative of a complex value of a differentsecond polarization component of the modulated optical carrier at thesampling time; and a digital processor connected to receive the vectorsand being configured to perform a rotation on each received vectorindividually in a manner that compensates for polarization rotationsproduced by transmitting the modulated optical carrier from an opticaltransmitter thereof to the optical receiver.
 2. The apparatus of claim1, wherein the digital processor is configured to iteratively updateeach angle of the rotation by an amount proportional to a differencebetween magnitudes of the components of a vector produced by an earlierone of the rotations.
 3. The apparatus of claim 1, wherein the digitalprocessor is configured to rotate the received vectors withoutperforming cross equalization between the first and second components ofthe vectors.
 4. The apparatus of claim 1, wherein the processor isconfigured to perform the rotations in a manner that tends to equalizeamplitudes of the first second components.
 5. The apparatus of claim 2,wherein the digital processor is configured to evaluate an error in theamplitude of one of the components of the rotated vectors.
 6. Theapparatus of claim 2, wherein the digital processor is configured toequalize the first components of the rotated vectors based ondifferential phase errors of successive ones of the first components ofthe rotated vectors.
 7. The apparatus of claim 6, wherein the digitalprocessor is configured to equalize the second components of the rotatedvectors based on differential phase errors between successive ones ofthe second components of the rotated vectors.
 8. The apparatus of claim6, wherein the digital processor comprises a FIR filter, the FIR filterbeing configured to equalize the first components of the rotated vectorsby forming a weighted sum of (2L+1) successive ones of the firstcomponents of the rotated vectors, the number L being greater than orequal to one.
 9. The apparatus of claim 1, wherein the optical detectorcomprises: an optical hybrid configured to output first mixtures of themodulated optical carrier and a reference optical carrier at firstoutputs and to output second mixtures of the carriers having differentrelative phases at second outputs.
 10. The apparatus of claim 9, whereinthe digital processor is configured to equalize the first components ofthe rotated vectors based on evaluated differential phase errors betweensuccessive ones of the first components of the rotated vectors.
 11. Anapparatus, comprising: an optical receiver configured to recover dataPSK modulated onto a received optical carrier, the optical receivercomprising: an optical detector being configured to produce a sequenceof vectors having first digital electrical signal components, each firstelectrical digital signal component being indicative of a value of onepolarization component of the received optical carrier at acorresponding sampling time; and a digital signal processor beingconnected to receive the first digital electrical signal components andto equalize the first digital electrical signal components in a mannerresponsive to differential phases error between successive ones of thefirst digital electrical signal components.
 12. The apparatus of claim11, wherein the optical detector is configured to produce second digitalelectrical signal components of the vectors, each second digitalelectrical signal component being indicative of a value of anotherpolarization component of the received optical carrier at thecorresponding sampling time; and wherein the digital processor isconfigured to equalize the second digital electrical signal componentsin a manner responsive to differential phases error between successiveones of the second digital electrical signal components.
 13. Theapparatus of claim 11, wherein the digital processor comprises a deviceconfigured to function as a FIR filter that equalizes the first digitalelectrical signal components by producing a weighted sum of (2L+1)successive ones of the first digital electrical signal components, Lbeing greater than or equal to one.
 14. The apparatus of claim 13,wherein the digital processor further comprises a weight updating devicethat is configured to update weights defining the sum based on thedifferential phase error.
 15. A method for operating an opticalreceiver, comprising: at each of a sequence of sampling times, producinga first 2D complex digital signal vector whose first component isindicative of a phase and amplitude of one polarization component of amodulated optical carrier and whose second component is indicative of aphase and amplitude of another polarization component of the carrier;and for each one of the sampling times, constructing a second 2D complexdigital signal vector that is a rotation of the first 2D complex digitalvector for the one of the sampling times, the rotation compensating apolarization rotation produced by transmission of the modulated opticalcarrier between an optical transmitter and the optical receiver.
 16. Themethod of claim 15, further comprising iteratively updating each angleof the rotation by an amount proportional to a difference betweenmagnitudes of the components of a vector produced by an earlier one ofthe rotations.
 17. The method of claim 15, further comprising prior toone of the acts of constructing, updating a form of the rotation for theone of the acts of constructing such that said one of the acts ofconstructing produces a second 2D complex digital signal vector whosefirst and second components have better equalized amplitudes.
 17. Themethod of claim 15, further comprising: equalizing first components ofthe second 2D digital signal complex vectors based on differential phaseerrors between successive ones of the first components of the second 2Dcomplex digital signal vectors.
 18. The method of claim 17, wherein theequalizing of each first component comprises producing a weighted sum of(2L+1) successive ones of the first components of the second 2D complexdigital signal vectors, L being greater than or equal to one.
 19. Themethod of claim 15, further comprising: separating the one polarizationcomponent of the received optical carrier from the another polarizationcomponent of the received optical carrier; mixing the separated onepolarization component with a reference optical carrier in a first pairof optical mixers; mixing the separated another polarization componentwith the reference optical carrier in a second pair of optical mixers;evaluating the first components of the first 2D complex digital signalvectors by sampling intensities of light output by the first pair ofoptical mixers at the sampling times in response to the mixing; andevaluating the second components of the first 2D complex digital signalvectors by sampling intensities of light output by the second pair ofoptical mixers at the sampling times in response to the mixing.
 20. Themethod of claim 19, wherein for each one of the pairs, the act of mixingmixes the reference and received optical carrier in a first of themixers of the one of the pairs with a relative phase shift that differsfrom a relative phase shift between the reference and received opticalcarriers in a second of the mixers of the one of the pairs by a phasebetween π/3 and 2π/3 modulo π.